I dont know where this whole "tube amps and LCDs dont mix" canard comes from.
One of the best combos, as per many reviews, is the LCD-2 and Alo Pan Am.
And as I type this, I am listening to the LCD2s on a 2A3 single-ended tube amp right now and I can assure you - it sounds absolutely gorgeous! If you want bright, in-your-face highs, you wont get it. But if you want a sound that comes close to what you hear in a concert hall, this is the way to go. I have Ozawa's "Rite of Spring" playing right now and it sounds *divine*.
Try the LCDs with a pair of single-ended triode tube amps. Single stage, zero feedback designs, preferably off a 2A3 or a 45 tube. Avoid the push-pull designs. You might be surprised.